Thread: differential form and wedge product

1. differential form and wedge product

Hello,

i have a little question: If f is a differential form. Is then $f \wedge f=0$?

I think so, but i'm not sure, because i never work with forms before. Here is my proof:

let f:M->\Lambda(M) be a k-form and T^k the Alternator. then we get
$(f \wedge f)(P)=f(p)\wedge f(p)=\frac{(2k)!}{k!k!}*T^{2k}(f(p)\otimes f(p))=0$
because $T^{2k}(f(p)\otimes f(p))=0$

Is this correct?

Regards

2. $\sigma = dx \wedge dy + dz \wedge dw$
$\sigma \wedge \sigma = (dx \wedge dy + dz \wedge dw)\wedge(dx \wedge dy + dz \wedge dw)$
$=dx \wedge dy \wedge dz \wedge dw + dz \wedge dw \wedge dx \wedge dy$
$=2 dx \wedge dy \wedge dz \wedge dw$

3. Hello,

thank you very much. Can you tell me why this is a differential form?
Can i also think of $f=e_1 \wedge e_2 + e_3 \wedge e_4$??

Regards

4. What is your definition of a differential form?

5. Our definition is:

A differential form is a smooth section of the natural projection.

Thanks